# The Naked Scientists Forum

### Author Topic: How does time dilation vary with gravity and distance?  (Read 2648 times)

#### jeffreyH

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##### How does time dilation vary with gravity and distance?
« on: 15/09/2013 00:20:27 »
Are there any plots of time dilation with respect to planetary mass and distance from the planet surface? Which equations would be used to calculate this?
« Last Edit: 15/09/2013 23:06:27 by chris »

#### Pmb

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##### Re: time dilation under gravity
« Reply #1 on: 15/09/2013 03:08:57 »
Are there any plots of time dilation with respect to planetary mass and distance from the planet surface? Which equations would be used to calculate this?
There may be but you'd have to do some work finding it. A friend of mine is writing a new version of his well known text Exploring Black Holes which is online at http://exploringblackholes.com

Hey! Nobody said that learning meant that everything was going to be handed to you on a silver platter ... at least not until I create such a website. ;)

#### jeffreyH

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##### Re: time dilation under gravity
« Reply #2 on: 15/09/2013 03:38:54 »
It's OK I found the wolfram time dilation calculator and managed to crash it! I did calculate this years ago using gamma etc in Excel but very rusty now. The reason I am looking is to explore overlapping gravitational potentials. I have noticed something interesting in the exoplanet database which may be significant.

#### jeffreyH

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##### Re: time dilation under gravity
« Reply #3 on: 15/09/2013 03:40:02 »
Are there any plots of time dilation with respect to planetary mass and distance from the planet surface? Which equations would be used to calculate this?
There may be but you'd have to do some work finding it. A friend of mine is writing a new version of his well known text Exploring Black Holes which is online at http://exploringblackholes.com

Hey! Nobody said that learning meant that everything was going to be handed to you on a silver platter ... at least not until I create such a website. ;)

I'll have a look at the sight. Thanks for the info.

#### Pmb

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##### Re: time dilation under gravity
« Reply #4 on: 15/09/2013 07:11:44 »
Quote from: jeffreyH
I'll have a look at the sight. Thanks for the info.
You're very welcome. There's a general relationship between redshift versus height using an arbitrary gravitational field. It'd take some time to do the math though. Even more time to create an entire page to illustrate the concept. I don't mind doing it if you think it would be of great help to you. Please let me know.

#### jeffreyH

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##### Re: time dilation under gravity
« Reply #5 on: 15/09/2013 19:22:13 »
Quote from: jeffreyH
I'll have a look at the sight. Thanks for the info.
You're very welcome. There's a general relationship between redshift versus height using an arbitrary gravitational field. It'd take some time to do the math though. Even more time to create an entire page to illustrate the concept. I don't mind doing it if you think it would be of great help to you. Please let me know.

I am not sure my thinking on this is right yet. The hollow planet argument raised issues that may invalidate my ideas.

#### Pmb

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##### Re: time dilation under gravity
« Reply #6 on: 15/09/2013 19:43:56 »
Quote from: jeffreyH
I'll have a look at the sight. Thanks for the info.
You're very welcome. There's a general relationship between redshift versus height using an arbitrary gravitational field. It'd take some time to do the math though. Even more time to create an entire page to illustrate the concept. I don't mind doing it if you think it would be of great help to you. Please let me know.
I am not sure my thinking on this is right yet. The hollow planet argument raised issues that may invalidate my ideas.
What issues are these? Keep in mind that so long as the total mass of the shell is the same mass as the ball with the same radius then the field outside the two are identical in every single way.

#### jeffreyH

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##### Re: time dilation under gravity
« Reply #7 on: 16/09/2013 00:13:50 »
Quote from: jeffreyH
I'll have a look at the sight. Thanks for the info.
You're very welcome. There's a general relationship between redshift versus height using an arbitrary gravitational field. It'd take some time to do the math though. Even more time to create an entire page to illustrate the concept. I don't mind doing it if you think it would be of great help to you. Please let me know.
I am not sure my thinking on this is right yet. The hollow planet argument raised issues that may invalidate my ideas.
What issues are these? Keep in mind that so long as the total mass of the shell is the same mass as the ball with the same radius then the field outside the two are identical in every single way.

Take the idealized situation where a mass is compressed exactly at the Schwarzschild radius. Take also the mass as uncompressed as a comparison. Find the point from the center of mass where for both objects time dilation is X. I imagine this distance would be the same for both situations but this is what I initially want to resolve. Is this already known?

#### Pmb

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##### Re: How does time dilation vary with gravity and distance?
« Reply #8 on: 16/09/2013 00:32:11 »
Quote from: jeffreyH
Sorry, but you totally lost me.

#### jeffreyH

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##### Re: How does time dilation vary with gravity and distance?
« Reply #9 on: 16/09/2013 17:26:57 »
Quote from: jeffreyH
Sorry, but you totally lost me.

OK sorry. Say we have a body orbiting a star at distance x in an ideal circular orbit. It will have time dilation y due to its orbital velocity and the influence of gravity. If this star is then compressed to the size of the event horizon (again idealized with no mass loss) would the orbiting body in the same orbit exhibit the same time dilation. I.E., No amplification due to compression. I think it would be the same.

#### jeffreyH

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##### Re: How does time dilation vary with gravity and distance?
« Reply #10 on: 17/09/2013 01:51:13 »
I've just done a google search for 'gravity amplification'. Boy was that a mistake.

However this did pop up.

http://physicsbuzz.physicscentral.com/2009/10/black-hole-loses-its-shirt.html

« Last Edit: 17/09/2013 02:08:01 by jeffreyH »

#### jeffreyH

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##### Re: How does time dilation vary with gravity and distance?
« Reply #11 on: 17/09/2013 02:32:26 »
The hollow planet got me musing. If you had a star that was large enough to collapse under its own gravitation once it had exhausted its fuel, but was surrounded by several orbiting stars that were just under this limit. Could the effect of the combined gravitation of the orbiting stars cancel out enough of the central stars internal gravitation to prevent collapse?

If so could this be balanced to allow a partial collapse?

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##### Re: How does time dilation vary with gravity and distance?
« Reply #11 on: 17/09/2013 02:32:26 »